1994final

# 1994final - SCARBOROUGH CAMPUS UNIVERSITY OF TORONTO...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: SCARBOROUGH CAMPUS UNIVERSITY OF TORONTO MATA26Y April 19, 1995 FINAL EXAMINATION 1. Evaluate the following integrals exactly if they exist. [4] (a) Z sin x √ 2 + cos x dx [4] (b) Z ∞ 2 1 4 + z 2 dz [4] (c) Z 1 a x + a- x dx , where a is a positive real number. [4] (d) Z e 1 9 x 2 ln xdx [4] 2. (a) Evaluate F ( x ) = Z x π/ 2 ( t + 1)cos2 tdt . [3] (b) Verify your answer to (a) by differentiating your expression for F ( x ). [4] 3. (a) State the first and secondversion of the Fundamental Theorem of Calculus. [4] (b) The function F ( x ) = R √ 9- x 2 e- t 2 2 dt has domain [- 3 , 3]. What are the values of F at the endpoints of that interval? Where is F decreasing/increasing? [9] 4. Determine the area of the region(s) enclosed by the curves y = x 2 and y = p | x | . Make a sketch! [4] 5. (a) State the trapezoidal rulefor numerical integration with error bound. [6] (b) The function f ( x ) = √ 1 + x 4 takes on the following values t 1 4 1 2 3 4 1 5 4 3 2 7 4 2 f ( t ) 1 1 . 002 1...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

1994final - SCARBOROUGH CAMPUS UNIVERSITY OF TORONTO...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online